- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Learning heat transport kernels using a nonlocal heat transport theory-informed neural network

Mufei Luo1,*, Charles Heaton1, Yizhen Wang1, Daniel Plummer1, Mila Fitzgerald1, Francesco Miniati2, Sam M. Vinko1, and Gianluca Gregori1

  • 1Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
  • 2Mach42, Robert Robinson Avenue, Oxford Science Park, Oxford OX4 4GP, United Kingdom

  • *Contact author: mufei.luo@physics.ox.ac.uk
PDF

Phys. Rev. Research 7, L042017 – Published 16 October, 2025

DOI: https://doi.org/10.1103/m215-3f6c

Abstract

We present a data-driven framework for the modeling of nonlocal heat transport in plasmas using a nonlocal theory-informed neural network trained on kinetic particle-in-cell simulations that span both local and nonlocal regimes. The model learns spatio-temporal heat flux kernels directly from simulation data, capturing dynamic transport behaviors beyond the reach of classical formulations. Unlike time-independent kernel models such as Luciani-Mora-Virmont and Schurtz-Nicolaï-Busquet models, our approach yields physically grounded, time-evolving kernels that adapt to varying plasma conditions. The resulting predictions show strong agreement with kinetic benchmarks across regimes. This offers a promising direction for data-driven modeling of nonlocal heat transport and contributes to a deeper understanding of plasma dynamics.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (36)

  1. G. Gregori, S. H. Glenzer, J. Knight, C. Niemann, D. Price, D. H. Froula, M. J. Edwards, R. P. J. Town, A. Brantov, W. Rozmus, and V. Y. Bychenkov, Effect of nonlocal transport on heat-wave propagation, Phys. Rev. Lett. 92, 205006 (2004).
  2. C. Arran, M. Holec, M. Sherlock, M. Marinak, and C. P. Ridgers, The accuracy of multi-group models for nonlocal electron transport in magnetized plasmas, Phys. Plasmas 32, 043908 (2025).
  3. O. A. Hurricane, P. K. Patel, R. Betti, D. H. Froula, S. P. Regan, S. A. Slutz, M. R. Gomez, and M. A. Sweeney, Physics principles of inertial confinement fusion and U.S. Program overview, Rev. Mod. Phys. 95, 025005 (2023).
  4. E. L. Yerger, M. W. Kunz, A. F. Bott, and A. Spitkovsky, Collisionless conduction in a high-beta plasma: A collision operator for whistler turbulence, J. Plasma Phys. 91, E20 (2025).
  5. S. Komarov, A. A. Schekochihin, E. Churazov, and A. Spitkovsky, Self-inhibiting thermal conduction in a high-β, whistler-unstable plasma, J. Plasma Phys. 84, 905840305 (2018).
  6. J. D. Huba, NRL Plasma Formulary (Naval Research Laboratory, Washington, DC, 2023).
  7. L. Spitzer and R. Härm, Transport phenomena in a completely ionized gas, Phys. Rev. 89, 977 (1953).
  8. A. V. Brantov, V. Y. Bychenkov, V. T. Tikhonchuk, and W. Rozmus, Nonlocal electron transport in laser heated plasmas, Phys. Plasmas 5, 2742 (1998).
  9. J. F. Luciani, P. Mora, and J. Virmont, Nonlocal heat transport due to steep temperature gradients, Phys. Rev. Lett. 51, 1664 (1983).
  10. G. P. Schurtz, P. D. Nicolaï, and M. Busquet, A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes, Phys. Plasmas 7, 4238 (2000).
  11. M. Sherlock, J. P. Brodrick, and C. P. Ridgers, A comparison of non-local electron transport models for laser-plasmas relevant to inertial confinement fusion, Phys. Plasmas 24, 082706 (2017).
  12. W. Q. Yuan, Z. H. Zhao, S. P. Zhu, X. T. He, and B. Qiao, Space-time dependent non-local thermal transport effects on laser ablation dynamics in inertial confinement fusion, Plasma Phys. Controlled Fusion 66, 045023 (2024).
  13. O. Michel, R. Duclous, P.-E. Masson-Laborde, C. Enaux, and P. Lafitte, A nonlocal electron transport model in the diffusion scaling of hydrodynamics, Phys. Plasmas 30, 022712 (2023).
  14. A. Chrisment, P. Loiseau, J.-L. Feugeas, P.-E. Masson-Laborde, J. Mathiaud, V. Tikhonchuk, and P. Nicolaï, Analysis of a kinetic model for electron heat transport in inertial confinement fusion plasmas, Phys. Plasmas 29, 062301 (2022).
  15. E. M. Epperlein and R. W. Short, A practical nonlocal model for electron heat transport in laser plasmas, Phys. Fluids B 3, 3092 (1991).
  16. O. V. Batishchev, V. Y. Bychenkov, F. Detering, W. Rozmus, R. Sydora, C. E. Capjack, and V. N. Novikov, Heat transport and electron distribution function in laser produced plasmas with hot spots, Phys. Plasmas 9, 2302 (2002).
  17. C. Lamy, B. Dubroca, P. Nicolaï, V. Tikhonchuk, and J.-L. Feugeas, Modeling of electron nonlocal transport in plasmas using artificial neural networks, Phys. Rev. E 105, 055201 (2022).
  18. F. Miniati and G. Gregori, Learning transport processes with machine intelligence, Sci. Rep. 12, 11709 (2022).
  19. A. R. Bell, R. G. Evans, and D. J. Nicholas, Elecron energy transport in steep temperature gradients in laser-produced plasmas, Phys. Rev. Lett. 46, 243 (1981).
  20. H. Zhao, S. Weng, Z. Sheng, S. Jin, and J. Zhang, A Vlasov-Fokker-Planck-Landau code for the simulation of colliding supersonic dense plasma flows, J. Comput. Phys. 503, 112843 (2024).
  21. A. R. Bell and M. Sherlock, The fast VFP code for solution of the Vlasov–Fokker–Planck equation, Plasma Phys. Controlled Fusion 66, 035014 (2024).
  22. Y. Sentoku, K. Mima, Y. Kishimoto, and M. Honda, Effects of relativistic binary collisions on PIC simulation of laser plasmas, J. Phys. Soc. Jpn. 67, 4084 (1998).
  23. Y. Sentoku and A. Kemp, Numerical methods for particle simulations at extreme densities and temperatures: Weighted particles, relativistic collisions and reduced currents, J. Comput. Phys. 227, 6846 (2008).
  24. A. J. Kemp, Y. Sentoku, V. Sotnikov, and S. C. Wilks, Collisional relaxation of superthermal electrons generated by relativistic laser pulses in dense plasma, Phys. Rev. Lett. 97, 235001 (2006).
  25. M. Sherlock, E. G. Hill, R. G. Evans, S. J. Rose, and W. Rozmus, In-depth plasma-wave heating of dense plasma irradiated by short laser pulses, Phys. Rev. Lett. 113, 255001 (2014).
  26. T. D. Arber, K. Bennett, C. S. Brady, A. Lawrence-Douglas, M. G. Ramsay, N. J. Sircombe, P. Gillies, R. G. Evans, H. Schmitz, A. R. Bell, and C. P. Ridgers, Contemporary particle-in-cell approach to laser-plasma modelling, Plasma Phys. Controlled Fusion 57, 113001 (2015).
  27. R. A. Fonseca, L. O. Silva, F. S. Tsung, V. K. Decyk, W. Lu, C. Ren, W. B. Mori, S. Deng, S. Lee, T. Katsouleas, and J. C. Adam, Osiris: A three-dimensional, fully relativistic particle in cell code for modeling plasma based accelerators, in Computational Science—ICCS 2002, edited by P. M. A. Sloot, A. G. Hoekstra, C. J. K. Tan, and J. J. Dongarra (Springer, Berlin, 2002), pp. 342–351.
  28. S. X. Hu, K. A. Nichols, N. R. Shaffer, B. Arnold, A. J. White, L. A. Collins, V. V. Karasiev, S. Zhang, V. N. Goncharov, R. C. Shah, D. I. Mihaylov, S. Jiang, and Y. Ping, A review on charged-particle transport modeling for laser direct-drive fusion, Phys. Plasmas 31, 040501 (2024).
  29. Z. Huang, C. Dong, and L. Wang, Machine-learning heat flux closure for multi-moment fluid modeling of nonlinear Landau damping, Proc. Natl. Acad. Sci. USA 122, e2419073122 (2025).
  30. E. R. Ingelsten, M. C. McGrae-Menge, E. P. Alves, and I. Pusztai, Data-driven discovery of a heat flux closure for electrostatic plasma phenomena, J. Plasma Phys. 91, E64 (2025).
  31. E. P. Alves and F. Fiuza, Data-driven discovery of reduced plasma physics models from fully kinetic simulations, Phys. Rev. Res. 4, 033192 (2022).
  32. A. Döpp, C. Eberle, S. Howard, F. Irshad, J. Lin, and M. Streeter, Data-driven science and machine learning methods in laser–plasma physics, High Power Laser Sci. Eng 11, e55 (2023).
  33. C. J. McDevitt and X. Tang, A physics-informed deep learning description of Knudsen layer reactivity reduction, Phys. Plasmas 31, 062701 (2024).
  34. D. D. Carvalho, D. R. Ferreira, and L. O. Silva, Learning the dynamics of a one-dimensional plasma model with graph neural networks, Mach. Learn.: Sci. Technol. 5, 025048 (2024).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/m215-3f6c for more details on the network configuration and model performance.
  36. J. P. Matte and J. Virmont, Electron heat transport down steep temperature gradients, Phys. Rev. Lett. 49, 1936 (1982).

Outline

Information

Phys. Rev. Research 7, L042017– Published 16 October, 2025
  • Received 13 June 2025
  • Accepted 24 September 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation